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Table B1

Asymptotic models.

Models Expression Remark
Series k f thermal conductivity fluid
k s thermal conductivity solid
Lower bound
Parallel k f thermal conductivity fluid
k s thermal conductivity solid
Upper bound
Maxwell lower bound [79] Solid medium with random distribution of small spheres
Maxwell upper bound [79] Solid medium with random distribution of small spheres. Dilute suspension
Bruggeman [80] The main approach of this theory assumes that a composite material may be constructed incrementally by introducing infinitesimal changes to an already existing material
Hamilton-Crosser [28] F: shape factor
V: volume fraction
Maxwell, Comprehensive equation, from Hadley [81] Mixture of two material powders
Miller upper bound, Symmetric cell material
for spherical cell shape
for plate cell shape
Miller lower bound, Symmetric cell material.
for spherical cell shape
for plate cell shape
Effective Medium Theory Developed from averaging the multiple values of the constituents that directly make up the composite material.
Hashin-Shtrikman [29] Variational theorems applied to the derivation of bounds for the effective thermal conductivity of macroscopically homogeneous and isotropic multiphase materials
Krischer [63] Packed bed of spheres.
A highly anisotropic structure is assumed

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